Probability aside, if this situation ever comes up, it'll be on Wheel of Fortune or some other yawntastic game show or a street-side entertainer. This will be only ONE instance, in which probability doesn't play a factor or matter a shit in my opinion. My advice would be to go with your gut instinct and keep the first one you picked.

Probability aside, if this situation ever comes up, it'll be on Wheel of Fortune or some other yawntastic game show or a street-side entertainer. This will be only ONE instance, in which probability doesn't play a factor or matter a shit in my opinion. My advice would be to go with your gut instinct and keep the first one you picked.

Pretty sure Wheel of Fortune only deals with words.. and just because it may only happen once in a life time, doesn't mean you shouldn't apply the same logic you apply to everything else. In fact, there me more of a reason to do so being a rare occurrence. Depends on how you look at it I suppose.

I think my original way of figuring this out was flawed, even if it was correct. I'm not sure I completely understand.. do you have a 2/3 chance at the end solely because one of the cups has been shown empty?

Not really. Basically, there are three choices: you can either pick the "good" box, or one of the "bad" boxes. If you picked the one of 2 "bad" boxes, then switch, you win. But if you picked the 1 "good" box, then switch, you lose. So assuming you switch, 2 possibilites result in a win, and 1 possibility results in a loss.

Excellent. I was hoping to be completely proved wrong, because I knew 2/3 was correct but I'd been looking for proof that switching is best, but everywhere I had looked people couldn't completely validate their answer.

It's all the same to me, because while the chances of success may theoretically change, the item within the box never changes boxes from start to finish. So while your chances get better or worse it's still all down to chance, no matter how many you're choosing from. Unless you're psychic.